A cat, which mass 2.5 kg walks on a uniform plank of 4.0m long and mass 6.0kg. Two sawhorses at 0.3m and 2.4m from its right end to support the plank as shown in figure. The cat walks on it from right to the left until a certain position where the plank just begin to tip. Calculate the position of the cat from the left sawhorse when the plank just begin to tip .

Explanation:

Let when cat reaches the point L distance from the right end , the plank starts turning about the left sawhorse.

The weight of the plank will at at middle point , ie at 2 m from the right end .

The plank will turn about the left sawhorse . Taking torque about this point of weight of the plank and weight of the cat , we have

2.5 g x ( L - 2.4 ) = 6 x g x ( 2.4 - 2.0 )

2.5 L - 6 = 14.4 - 12

2.5 L = 8.4

L = 3.36

position from left sawhorse = 3.36 - 2.4 = .96 m to the left of left sawhorse.